When placing a slip-supported tool like a packer in a well, it is desirable to have the slip segments positively constrained in a retracted position to keep from being peeled off the tool when passing through the fluid in the well and to help avoid premature setting of the tool in the well. One prior arrangement of this general type is disclosed in U.S. Pat. No. 3,232,347 and in that arrangement, the lower end of a setting sleeve fits over the upper ends of the slip segments to keep the latter from moving radially outward as the arrangement is being lowered into a well. After reaching a specified well location, the tubing string carrying the arrangement is manipulated through a number of steps in a predetermined sequence involving raising, rotating and lowering the string in order to move several intricate parts of the arrangement in freeing the slips segments for use. Once free from the constraint of the sleeve, spring bands acting radially outward urge the segments against the interior wall of the well casing.